Abstract

Among several methods developed for uniaxial alignment of metallic nanorods for optical applications, alignment by film stretching consists in embedding the rods in a transparent thin film of thermoplastic polymer, followed by simultaneous heating and uniaxial stretching of the composite film. As to the quantification of the resulting alignment, it has been limited to statistical calculations based on microscopic examination, which is incomplete, subject to errors due to geometric distortions of the scanning electron microscope images and destructive, since it involves cutting of samples. In contrast, we present in this paper a non-destructive quantification of the average orientation of the rods, based on a probabilistic approach combined with numerical simulations of absorbance spectra and spectrometric characterization of the composite film. Assuming electromagnetically non-interacting rods, we consider the longitudinal absorbance peak of their ensemble to consist of the superposition of their individual spectra that we obtain by numerical simulation using the size and shape adapted dielectric function of the metal and the finite difference time domain method. The accuracy of the solution depends on the number of discretization intervals, the accuracy of the numerical simulations, and the accurate knowledge of the polydispersity of the rods. For the sake of concreteness, we used nanorods to describe the quantification steps but the method is equally valid for any dichroic particles.

We wish to warmly thank Nicole A. MacDonald, physicist of Le Centre de Caractérisation Microscopique des Matériaux, Montreal, for her skilful efforts in taking the SEM images of the nanorods.

Article outline:I. INTRODUCTIONII. THE THEORETICAL QUANTIFICATION METHODA. IntroductionB. Simplifying assumptionsC. A unified probabilistic approachD. Problem formulation and its solutionE. Implementation of the method for the discretized problem1. Parameters defining the Gaussian distribution2. Discretization of the domain3. Solving for the average orientational angle 4. Summary and conclusions